Vehicles include an exhaust gas treatment system for treating a flow of exhaust gas from an engine. The exhaust gas treatment system may include one or more structures that collect soot therein, such as but not limited to, a particulate filter. When the engine includes a diesel engine, the particulate filter is often referred to as a diesel particulate filter. The amount of soot that the engine produces varies as the operating states of the engine change, e.g., the engine may produce more soot when operating under a heavy load, then when operating under a light load. In order to properly control and/or monitor the exhaust gas treatment system, the vehicle must estimate the amount of soot that the engine produces. For example, the exhaust gas treatment system may include a soot sensor disposed downstream of the particulate filter. The soot sensor senses the amount of soot remaining in the flow of exhaust gas downstream from the particulate filter. However, in order to determine if the particulate filter is functioning properly, the vehicle must estimate how much soot is being introduced into the flow of exhaust gas from the engine, upstream of the particulate filter, to be able to determine an acceptable level of soot in the flow of exhaust gas downstream of the particulate filter. The estimated amount of soot produced by the engine may also be used to determine when to initiate regeneration of the particulate filter.